The concept of shortcuts to adiabaticity (STA) [1]}, [2]} is proposed, which combines the advantages of both adiabatic passages and resonant pulses. It breaks the adiabatic regime by various techniques, including inverse engineering [3]}, counter-diabatic driving [4]}, [5]}, fast-forward scaling [6]}, [7]}, which has been well developed over the past decade. Specifically, inverse engineering emanates from the Lewis-Riesenfeld theory, allowing superadiabatic state evolution on dynamical modes with boundary conditions. In addition, inverse engineering leaves enough freedom to further allow other tasks such as, e.g., suppressing systematic errors by collaborating with optimal control theory [8]}, [9]}, [10]}, dynamical decoupling techniques [11]}, and machine learning methods [12]}, [13]}, [14]}. However, invariant-based STA requires continuously tunable parameters, limiting the genre of quantum control as analog-only. We consider a more complicated task: designing digital pulses instead of an analog controller with the same output and similar features. In this manner, we would deliver a framework that can be naturally integrated in current quantum computing paradigms based on the application of several digital quantum gates.
